The positioning system for positioning a vehicle conventionally performs a positioning process in the following manner. That is, an in-vehicle device in the positioning system detects a signal intensity of a received signal (i.e., Received Signal Strength Indicator (RSSI)), and generates travel locus information that associates the RSSI with a travel locus. Then, the in-vehicle device compares the travel locus information with reference locus information (i.e., reference locus information: associating a distance between a reference position closes to a reference station and a subject vehicle with RSSI), for estimating the position of the vehicle. (See for example, a patent document, Japanese Patent Laid-Open No. JP 2013-257306.)